Calculate the radius of the circumference obtained by using a compass whose arms measure 10 cm if they form an angle of 50° with each other.

To calculate the radius of the circumference described by a compass with 10 cm long arms forming a 50° angle, we use the formula provided:

Given:
Arm length, a = 10 \, \text{cm}
Angle, \theta = 50^\circ

Using the formula:
r = a \times \sin\left(\frac{\theta}{2}\right)

Substitute the given values:
r = 10 \times \sin\left(\frac{50^\circ}{2}\right)
r = 10 \times \sin\left(25^\circ\right)

Now, calculate the sine value:
r = 10 \times \sin\left(25^\circ\right) \approx 10 \times 0.423

\boxed{r \approx 4.23 \, \text{cm}}

Therefore, the radius of the circumference that can be drawn with a compass set to 10 cm arms, forming a 50° angle, is approximately 4.23 cm.